ABSTRACT
Much of the algebra used in experimental reports in psychophysics is simply the general linear regression model in one (or rarely more) variables. The original model which is used as a starting point was developed to give a coherent framework, within which a diversity of phenomena associated with the perception of the intensity of a unidimensional sensory input could be accommodated. It is necessary to make some strong simple assumptions on how a double, or multiple, loop could work. Mathematically it is an unexplored problem, and given the nonlinearity of the recursion some paradoxical behavior is to be for some values. A naive and mistaken mathematical notion about nonlinear modelling is that “nonlinear equations can fit anything, and so violate the principle that they should be potentially refutable by some observable data set.”. The identification depends on the local computability of fractal dimensionality or of the Lyapunov coefficients for at least one dimension.
